Physical Definition

The physical definition of a case includes the definition of the free-stream, the reference values and the non-dimensionalization. SU2 offers different ways of setting and computing this definition. This document gives a short overview on the config options and their physical relation.

Fluid Model

Solver Version
EULER, NAVIER_STOKES, RANS, NEMO_EULER, NEMO_NAVIER_STOKES, INC_EULER, INC_NAVIER_STOKES, INC_RANS, FEM_EULER, FEM_NAVIER_STOKES 7.0.0

For fluid simulations, a model defining the equation of state and thermodynamic properties of the fluid or mixture is required. This is selected using the FLUID_MODEL option in the config. Available fluid models in SU2 include:

Option Value Description
STANDARD_AIR Air model with ideal gas EOS
IDEAL_GAS Arbitrary fluid with ideal gas EOS
VW_GAS Arbitrary fluid with Vander-Waals EOS
PR_GAS Arbitrary fluid with Peng-Robinson EOS
CONSTANT_DENSITY Constant density
INC_IDEAL_GAS Incompressible fluid constant specific heat
INC_IDEAL_GAS_POLY Incompressible fluid polynomial specific heat
FLUID_MIXTURE Incompressible ideal gas mixing laws for multicomponent flow
SU2_NONEQ SU2 nonequilibrium thermochemical library
MUTATIONPP Mutation++ nonequilibrium thermochemical library

Some fluid models require the specification of additional parameters, with the full set of required options available in the configuration file template.

Reference Values

Solver Version
EULER, NAVIER_STOKES, RANS, INC_EULER, INC_NAVIER_STOKES, INC_RANS, FEM_EULER, FEM_NAVIER_STOKES 7.0.0

The following table depicts the reference values used by most of the solvers in SU2. The highlighted variables vary depending on the actual solver and the user input.

Variable Unit Reference
Length \(m\) \(l_{ref} = 1\)
Density \(\frac{kg}{m^3}\) \(\rho_{ref}\) (based on user input)
Velocity \(\frac{m}{s}\) \(v_{ref}\) (based on user input)
Temperature \(K\) \(T_{ref}\) (based on user input)
Pressure \(Pa\) \(p_{ref}\) (based on user input)
Viscosity \(\frac{kg}{ms}\) \(\mu_{ref} = \rho_{ref}v_{ref}l_{ref}\)
Time \(s\) \(t_{ref} = \frac{l_{ref}}{v_{ref}}\)
Heatflux \(\frac{W}{m^2}\) \(Q_{ref} = \rho_{ref}v^3_{ref}\)
Gas Constant \(\frac{m^2}{s^2 K}\) \(R_{ref} = \frac{v^2_{ref}}{T_{ref}}\)
Conductivity \(\frac{W}{mK}\) \(k_{ref} = \mu_{ref}R_{ref}\)
Force \(N\) \(F_{ref} = \rho_{ref}v^2_{ref}l^2_{ref}\)

Free-Stream Definition (Compressible)

Solver Version
EULER, NAVIER_STOKES, RANS,FEM_EULER, FEM_NAVIER_STOKES 7.0.0

The physical definition for the compressible solvers in SU2 based around the definition of the free-stream. The free-stream values are not only used as boundary conditions for the MARKER_FAR option, but also for initialization and non-dimensionalization. That means even if you don’t have any farfield BCs in your problem, it might be important to prescribe physically meaningful values for the options.

Thermodynamic State

The thermodynamic state of the free-stream is defined by the pressure \(p_{\infty}\), the density \(\rho_{\infty}\) and the temperature \(T_{\infty}\). Since these quantities are not independent, only two of these values have to be described and the third one can be computed by an equation of state, depending on the fluid model used. There are two possible ways implemented that can be set using FREESTREAM_OPTION:

  • TEMPERATURE_FS (default): Density \(\rho_{\infty}\) is computed using the specified pressure \(p_{\infty}\) (FREESTREAM_PRESSURE) and temperature \(T_{\infty}\) (FREESTREAM_TEMPERATURE).
  • DENSITY_FS: Temperature \(T_{\infty}\) is computed using the specified pressure \(p_{\infty}\) (FREESTREAM_PRESSURE) and density \(\rho_{\infty}\) (FREESTREAM_DENSITY).

Mach Number and Velocity

The free-stream velocity \(v_{\infty}\) is always computed from the specified Mach number \(Ma_{\infty}\) (MACH_NUMBER) and the computed thermodynamic state. The flow direction is based on the angle of attack (AOA) and the side-slip angle (SIDESLIP_ANGLE, for 3D).

Reynolds Number and Viscosity

If it is a viscous computation, by default the pressure \(p_{\infty}\) will be recomputed from a density \(\rho_{\infty}\) that is found from the specified Reynolds number \(Re\) (REYNOLDS_NUMBER). Note that for an ideal gas this does not change the Mach number \(Ma_{\infty}\) as it is only a function of the temperature \(T_{\infty}\). If you still want to use the thermodynamic state for the free-stream definition, set the option INIT_OPTION to TD_CONDITIONS (default: REYNOLDS). In both cases, the viscosity is computed from the dimensional version of Sutherland’s law or the constant viscosity (FREESTREAM_VISCOSITY), depending on the VISCOSITY_MODEL option.

Non-Dimensionalization

For all schemes, as reference values for the density and temperature the free-stream values are used, i.e. \(\rho_{ref} = \rho_{\infty}, T_{ref} = T_{\infty}\). The reference velocity is based on the speed of sound defined by the reference state: \(v_{ref} = \sqrt{\frac{p_{ref}}{\rho_{ref}}}\). The dimensionalization scheme can be set using the option REF_DIMENSIONALIZATION and defines how the reference pressure \(p_{ref}\) is computed:

  • DIMENSIONAL: All reference values are set to 1.0, i.e. the computation is dimensional.
  • FREESTREAM_PRESS_EQ_ONE: Reference pressure equals free-stream pressure, \(p_{ref} = p_{\infty}\).
  • FREESTREAM_VEL_EQ_MACH: Reference pressure is chosen such that the non-dimensional free-stream velocity equals the Mach number: \(p_{ref} = \gamma p_{\infty}\).
  • FREESTREAM_VEL_EQ_ONE: Reference pressure is chosen such that the non-dimensional free-stream velocity equals 1.0: \(p_{ref} = Ma^2_{\infty} \gamma p_{\infty}\).

Free-Stream Definition (Thermochemical Nonequilibrium)

Solver Version
NEMO_EULER, NEMO_NAVIER_STOKES 7.0.0

The physical definition for the thermochemical nonequilibrium (NEMO) solvers is similar to the compressible solvers, but with additional parameters to specify. The free-stream values are not only used as boundary conditions for the MARKER_FAR option, but also for initialization and non-dimensionalization. That means even if you don’t have any farfield BCs in your problem, it might be important to prescribe physically meaningful values for the options.

Free-Stream Temperatures

Thermodynamic state is specified using the same options as the compressible solver, with the addition of the free-stream electronic temperature. This can be specified using the FREESTREAM_TEMPERATURE_VE option in the config file. For a free-stream in equilibrium, this is typically the same value as specified in the FREESTREAM_TEMPERATURE option.

Chemical Composition and Mass Fractions

The NEMO solvers require a specification of thermochemical nonequilibrium library using the FLUID_MODEL option, either SU2_NONEQ if using the SU2 built-in thermochemical library, or MUTATIONPP if using the Mutation++ thermochemical library.

A chemistry model, consisting of a set of flow species, thermochemical properties, and chemical reactions, is specified using GAS_MODEL. The names of these models are specific to the thermochemical library. If using the SU2_NONEQ option the choices are ARGON, N2, AIR-5, and AIR-7.

Free-stream mass fractions must also be specified in list using the option GAS_COMPOSITION. The mass fractions are specified as decimal values in the order of the species in the gas model. For example, an AIR-5 mixture of 77% oxygen and 23% nitrogen would be expressed as (0.77, 0.23, 0.00, 0.00, 0.00).

Transport Coefficient Model (Thermochemical Nonequilibrium)

Solver Version
NEMO_NAVIER_STOKES 7.0.0

A transport coefficient model must be specified for viscous simulations with the NEMO solver, using the TRANSPORT_COEFF_MODEL config option. Available options when using the SU2TCLib thermochemical library are the Wilkes-Blottner-Eucken, Gupta-Yos, and Sutherland viscosity models, specified by WILKE, GUPTA-YOS, and SUTHERLAND, respectively. The default option for transport coefficient model is Wilkes-Blottner-Eucken.

It should be noted the Sutherland model is only used to evaluate viscosity, and the Wilkes-Blottner-Eucken model is used to evaluate diffusion coefficient and thermal conductivity.

Flow Condition (Incompressible)

Solver Version
INC_EULER, INC_NAVIER_STOKES, INC_RANS 7.0.0

The physical definition of the incompressible solvers is accomplished by setting an appropriate flow condition for initialization and non-dimensionalization. SU2 solves the incompressible Navier-Stokes equations in a general form allowing for variable density due to heat transfer through the low-Mach approximation (or incompressible ideal gas formulation).

Thermodynamic and Gauge Pressure

In the incompressible problem the thermodynamic pressure is decoupled from the governing equations and density is therefore only a function of temperature variations. The absolute value of the pressure is not important and any reference to the pressure \(p\) is considered as the gauge value, i.e. it is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus (an arbitrary) atmospheric pressure.

Initial State and Non-Dimensionalization

The initial state, i.e. the initial values of density \(\rho_0\), velocity vector \(\bar{v}_{0}\) and temperature \(T_0\) are set with INC_DENSITY_INIT, INC_VELOCITY_INIT and INC_TEMPERATURE_INIT, respectively. The initial pressure \(p_0\) is always set to 0.0.

The reference values \(\rho_{ref}, T_{ref}, v_{ref}\) equal the initial state values by default (or if INC_NONDIM= INITIAL_VALUES). If INC_NONDIM is set to REFERENCE_VALUES you can define different values for them using the options INC_DENSITY_REF, INC_VELOCITY_REF and INC_TEMPERATURE_REF. The reference pressure is always computed by \(p_{ref} = \rho_{ref}v^2_{ref}\).

Note: The initial state is also used as boundary conditions for MARKER_FAR.

Turbulence Models

Set SOLVER= RANS or SOLVER= INC_RANS, and choose the model with KIND_TURB_MODEL= SA or KIND_TURB_MODEL= SST. Choose the variant with SA_OPTIONS or SST_OPTIONS. The defaults are SA without the ft2 term and SST-2003m. Turbulence Models lists all variants, the free-stream and inlet values, and where SU2 differs from the literature.

Transition Models

Set KIND_TRANS_MODEL= LM for the Langtry-Menter model, with SST or SA, and choose the version and correlation with LM_OPTIONS. For the algebraic SA-BCM model, set KIND_TURB_MODEL= SA and SA_OPTIONS= BCM. Transition Models describes both models and their options.


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